(*) Let \(G\) be a finite group and \(f,g : G \rightarrow \mathbb{C}\). Show that
\[\widehat{f \ast g} = \hat{f} \cdot \hat{g},\]
where the Fourier transform \(\hat{f}\) and convolution \(\ast\) were defined in class.

(**) Calculate numerically and plot the histogram of zeros
of Hermite polynomial of a large order \(N\). Submit your code
printout and a picture. Hint: it is nicer to have \(N\) fairly
large, about 500. But the straightforward way (defining the
polynomial, finding its roots) will not work because the
coefficients grow too fast. Recast the problem as looking for
eigenvalues of a matrix instead (check the typed lecture
notes!).